Eight-queens problem: Consider the classic puzzle of placing eight queens on an 8 8 chessboard so that no two queens are in the same row or in the same column or on the same diagonal. How many different solutions are there so: a. no two queens are on the same square? b. no two queens are in the same row? c. no two queens are in the same row or in the same column? Also estimate how long it would take to find all the solutions to the problem by exhaustive search based on each of these approaches on a computer capable of checking 10 billion positions per second.